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lfunc_lfunctions • Show schema
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{'Lhash': '740378933596658405324223681105', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5, -0.8660254037844386], 'a4': [1.0, 1.7320508075688772], 'a5': [-3.4641016151377544, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, 1.5], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.22', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '2584274991253897458534789914505', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-1.0, -1.7320508075688772]], [[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [3.4641016151377544, 0], [5.0, 0]], [[1.0, 0], [-0.8660254037844386, -1.5], [-3.5, 6.06217782649107]], [[1.0, 0], [1.7320508075688772, -3.0], [-5.5, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '13.9', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/e/f/22/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-507-13.9-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-507-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': -0.28039600339821724, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58405599576362733940293168372', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '740378933596658405324223681105', 'Lhash_array': ['740378933596658405324223681105'], 'label': '2-507-13.9-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/e/f/22/1'}